A Bootstrapping Market Implied Moment Matching Calibration for Models with Time-Dependent Parameters

Abstract

This paper extends the moment matching market implied calibration procedure to Markov models with piecewise constant parameters between successive quoted option maturities. The Markov property allows us to determine the parameter set of each subprocess by a bootstrapping moment matching calibration. This sequential calibration arises naturally due to the additive property of cumulants of independent random variables and consists in solving M independent moment matching systems of N equations, where M and N denote the number of quoted maturities and the number of parameters, respectively. For popular Lévy processes, these systems can be transformed into M systems of algebraic equations which give directly the N model parameters of each subprocess in terms of the second to the (N+1)th standardized moments of the log asset return process between successive maturity times. For the numerical study, we work out the bootstrapping moment matching calibration under two popular Lévy models with piecewise constant parameters, namely the VG and Meixner models and compare its performance with existing calibration procedures for term structure models.